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Learning Graph Normalization for Graph Neural Networks (2009.11746v1)

Published 24 Sep 2020 in cs.LG and cs.CV

Abstract: Graph Neural Networks (GNNs) have attracted considerable attention and have emerged as a new promising paradigm to process graph-structured data. GNNs are usually stacked to multiple layers and the node representations in each layer are computed through propagating and aggregating the neighboring node features with respect to the graph. By stacking to multiple layers, GNNs are able to capture the long-range dependencies among the data on the graph and thus bring performance improvements. To train a GNN with multiple layers effectively, some normalization techniques (e.g., node-wise normalization, batch-wise normalization) are necessary. However, the normalization techniques for GNNs are highly task-relevant and different application tasks prefer to different normalization techniques, which is hard to know in advance. To tackle this deficiency, in this paper, we propose to learn graph normalization by optimizing a weighted combination of normalization techniques at four different levels, including node-wise normalization, adjacency-wise normalization, graph-wise normalization, and batch-wise normalization, in which the adjacency-wise normalization and the graph-wise normalization are newly proposed in this paper to take into account the local structure and the global structure on the graph, respectively. By learning the optimal weights, we are able to automatically select a single best or a best combination of multiple normalizations for a specific task. We conduct extensive experiments on benchmark datasets for different tasks, including node classification, link prediction, graph classification and graph regression, and confirm that the learned graph normalization leads to competitive results and that the learned weights suggest the appropriate normalization techniques for the specific task. Source code is released here https://github.com/cyh1112/GraphNormalization.

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Authors (5)
  1. Yihao Chen (40 papers)
  2. Xin Tang (48 papers)
  3. Xianbiao Qi (38 papers)
  4. Chun-Guang Li (22 papers)
  5. Rong Xiao (44 papers)
Citations (47)

Summary

  • The paper introduces an adaptive framework that integrates node-wise, adjacency-wise, graph-wise, and batch-wise normalization tailored for GNNs.
  • It exploits both local and global graph structures to refine normalization and improve training efficiency.
  • Experimental results on benchmark datasets confirm that adaptive normalization consistently outperforms traditional methods in various graph tasks.

Learning Graph Normalization for Graph Neural Networks

Graph Neural Networks (GNNs) have become a focal point of research due to their efficacy in handling graph-structured data. These networks are instrumental in applications across domains such as natural language processing, computer vision, and social network analysis. The paper by Chen et al. aims to address a crucial aspect of GNNs — normalization, which is vital for effective training. Traditional neural networks benefit significantly from normalization techniques like batch normalization (BN) and layer normalization (LN), but for GNNs, these techniques often need adjustment to accommodate the non-Euclidean nature of graph data.

Problem Formulation

The key insight explored in this paper is that normalization in GNNs should consider the unique structural characteristics of graph data. GNNs typically model data by propagating and aggregating information across graph nodes and edges. However, various GNN applications might require different normalization techniques due to the diversity in graph structures and tasks. Existing normalization methods like BN, though useful, do not sufficiently exploit the local and global graph properties, hence limiting performance. This paper proposes a systematic approach to learning graph normalization, aiming to optimize the use of different normalization techniques specifically for GNNs.

Proposed Approach

Chen et al. introduce a novel framework for learning a suitable graph normalization by integrating multiple normalization methods: node-wise, adjacency-wise, graph-wise, and batch-wise normalization:

  1. Node-wise Normalization: Analogous to layer normalization, this method computes statistics (mean and variance) within each node individually.
  2. Adjacency-wise Normalization: This newly introduced method considers the local neighborhood of a node, computing statistics based on its adjacent nodes to maintain local structural information, which is often essential for tasks requiring high relational sensitivity.
  3. Graph-wise Normalization: Computes normalization statistics over an entire graph, preserving global graph structure, potentially useful for tasks that benefit from a holistic view of graph topology.
  4. Batch-wise Normalization: Similar to conventional batch normalization, applied over a batch of graphs, maintaining the advantages of BN in stabilizing training and accelerating convergence.

The learning framework involves optimizing a weighted combination of these normalization techniques, thus allowing the automatic selection of the most appropriate or effective combination for a given task.

Experimental Evaluation

The methodology was validated on a series of benchmark datasets covering diverse tasks such as node classification, link prediction, graph classification, and regression. The results indicate that:

  • GN\textsubscript{g} (graph-wise normalization) and GN\textsubscript{a} (adjacency-wise normalization) consistently outperform batch normalization in node classification tasks, demonstrating their effectiveness in leveraging graph structure.
  • GN\textsubscript{b} (batch-wise normalization), however, excels in graph classification and regression tasks, reflecting its utility where the holistic properties of batches are beneficial.
  • The adaptive framework (GN) achieves competitive performance across all tasks, indicating its potential as a universal normalization strategy for GNNs.

Implications and Future Directions

The contributions of this paper underline the importance of considering graph topology in the normalization process. The framework presented not only enhances the flexibility of GNNs but also suggests a pathway for further exploration in adaptive and task-specific learning strategies within graph-based models.

This paper supports the notion of a tailored approach to neural architecture design in machine learning, particularly for non-traditional data structures like graphs. Future work could extend this methodology to larger, more complex datasets, explore alternative formulations of adjacency or graph-wise normalization, or integrate this framework with different GNN architectures to further validate its applicability and robustness. In sum, the paper offers a compelling direction for rendering GNNs more effective and universally adaptable through strategic use of normalization.

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